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Non-staggered triangular grids have many advantages in performing river or ocean modeling with the finite-volume method. However, horizontal divergence errors may occur, especially in large-scale hydrostatic calculations with centrifugal acceleration. This paper proposes an unstructured finite-volume method with a filtered scheme to mitigate the divergence noise and avoid further influencing the velocities and water elevation. In hydrostatic pressure calculations, we apply the proposed method to three-dimensional curved channel flows. Approximations reduce the numerical errors after filtering the horizontal divergence operator, and the approximation is second-order accurate. Numerical results for the channel flow accurately calculate the velocity profile and surface elevation at different Froude numbers. Moreover, secondary flow features such as the vortex pattern and its movement along the channel sections are also well captured.
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This paper presents experimental and numerical studies on the erosion of a horizontal granular bed by a two-dimensional plane vertical impinging jet to predict the eroded craters’ size scaling (depth and width). The simulations help understand the microscopic processes that govern erosion in this complex flow. A modified jet-bed distance, accounting for the plane jet virtual origin, is successfully used to obtain a unique relationship between the crater size and a local Shields parameter. This work develops a two-phase flow numerical model to reproduce the experimental results. The numerical techniques are based on a finite volume formulation to approximate spatial derivatives, a projection technique to calculate the pressure and velocity for each phase, and a staggered grid to avoid spurious oscillations. Different options for the sediment’s solid-to-liquid transition during erosion are proposed, tested, and discussed. One model is based on unified equations of continuum mechanics, others on modified closure equations for viscosity or momentum transfer. A good agreement between the numerical solutions and the experimental measurements is obtained.
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Every year, in the Vietnam Mekong Delta Coastal Zone (VMDCZ), erosions cause approximately 300 ha of agricultural land loss. Therefore, measures for shoreline protection are urgently needed. This paper discusses the impacts of protection measures in the Go-Cong Coastal Zone to prevent erosion/accretion processes, predicted by two numerical models, MIKE21-FM and TELEMAC-2D. Hard and soft measures have been proposed using breakwaters and sandbars, respectively. The simulations show that the erosion/accretion trends provided by both models are similar. For breakwaters, MIKE21-FM provides less accretion than TELEMAC-2D in areas extending over 300 m and 500 m from shorelines. However, for sandbars, MIKE21-FM shows higher accretion within areas extending over 500 m but less than 300 m. Sandbars cause higher accretion in a larger area, extending over 1000 m offshore. The simulation results allow us to propose two alternative measures: (1) a row of several breakwater units will be implanted at 300 m offshore. The length of each unit is 600 m, with a gap between two neighbouring units of 70 m and a crest elevation of 2.2 m above mean sea level (MSL). (2) A row of sandbar units will be posed at 500 m offshore, with a unit length of 1000 m and a gap between the two neighbouring units of 200 m. The crest elevation is fixed at MSL.